Reassessing the human immunodeficiency virus type 1 life cycle through age-structured modeling: life span of infected cells, viral generation time, and basic reproductive number, R0

Engineered deletions of HIV replicate conditionally to reduce disease in nonhuman primates

Antiviral therapies with reduced frequencies of administration and high barriers to resistance remain a major goal. For HIV, theories have proposed that viral-deletion variants, which conditionally replicate with a basic reproductive ratio [R0] > 1 (termed "therapeutic interfering particles" or "TIPs"), could parasitize wild-type virus to constitute single-administration, escape-resistant antiviral therapies. We report the engineering of a TIP that, in rhesus macaques, reduces viremia of a highly pathogenic model of HIV by >3log10 following a single intravenous injection. Animal lifespan was significantly extended, TIPs conditionally replicated and were continually detected for >6 months, and sequencing data showed no evidence of viral escape. A single TIP injection also suppressed virus replication in humanized mice and cells from persons living with HIV. These data provide proof of concept for a potential new class of single-administration antiviral therapies.

Dynamic analysis of a cytokine-enhanced viral infection model with infection age

Recent studies reveal that pyroptosis is associated with the release of inflammatory cytokines which can attract more target cells to be infected. In this paper, a novel age-structured virus infection model incorporating cytokine-enhanced infection is investigated. The asymptotic smoothness of the semiflow is studied. With the help of characteristic equations and Lyapunov functionals, we have proved that both the local and global stabilities of the equilibria are completely determined by the threshold $ \mathcal{R}_0 $. The result shows that cytokine-enhanced viral infection also contributes to the basic reproduction number $ \mathcal{R}_0 $, implying that it may not be enough to eliminate the infection by decreasing the basic reproduction number of the model without considering the cytokine-enhanced viral infection mode. Numerical simulations are carried out to illustrate the theoretical results.

Dynamic analysis of an age structure model for oncolytic virus therapy

Cancer is recognized as one of the serious diseases threatening human health. Oncolytic therapy is a safe and effective new cancer treatment method. Considering the limited ability of uninfected tumor cells to infect and the age of infected tumor cells have a significant effect on oncolytic therapy, an age-structured model of oncolytic therapy involving Holling-Ⅱ functional response is proposed to investigate the theoretical significance of oncolytic therapy. First, the existence and uniqueness of the solution is obtained. Furthermore, the stability of the system is confirmed. Then, the local stability and global stability of infection-free homeostasis are studied. The uniform persistence and local stability of the infected state are studied. The global stability of the infected state is proved by constructing the Lyapunov function. Finally, the theoretical results are verified by numerical simulation. The results show that when the tumor cells are at the appropriate age, injection of the right amount of oncolytic virus can achieve the purpose of tumor treatment.

Quantifying mechanistic traits of influenza viral dynamics using in vitro data

When analysing in vitro data, growth kinetics of influenza virus strains are often compared by computing their growth rates, which are sometimes used as proxies for fitness. However, analogous to mathematical models for epidemics, the growth rate can be defined as a function of mechanistic traits: the basic reproduction number (the average number of cells each infected cell infects) and the mean generation time (the average length of a replication cycle). Fitting a model to previously published and newly generated data from experiments in human lung cells, we compared estimates of growth rate, reproduction number and generation time for six influenza A strains. Of four strains in previously published data, A/Canada/RV733/2003 (seasonal H1N1) had the lowest basic reproduction number, followed by A/Mexico/INDRE4487/2009 (pandemic H1N1), then A/Indonesia/05/2005 (spill-over H5N1) and A/Anhui/1/2013 (spill-over H7N9). This ordering of strains was preserved for both generation time and growth rate, suggesting a positive biological correlation between these quantities which have not been previously observed. We further investigated these potential correlations using data from reassortant viruses with different internal proteins (from A/England/195/2009 (pandemic H1N1) and A/Turkey/05/2005 (H5N1)), and the same surface proteins (from A/Puerto Rico/8/34 (lab-adapted H1N1)). Similar correlations between traits were observed for these viruses, confirming our initial findings and suggesting that these patterns were related to the degree of human adaptation of internal genes. Also, the model predicted that strains with a smaller basic reproduction number, shorter generation time and slower growth rate underwent more replication cycles by the time of peak viral load, potentially accumulating mutations more quickly. These results illustrate the utility of mathematical models in inferring traits driving observed differences in in vitro growth of influenza strains.

Environmental Restrictions: A New Concept Governing HIV-1 Spread Emerging from Integrated Experimental-Computational Analysis of Tissue-Like 3D Cultures

HIV-1 can use cell-free and cell-associated transmission modes to infect new target cells, but how the virus spreads in the infected host remains to be determined. We recently established 3D collagen cultures to study HIV-1 spread in tissue-like environments and applied iterative cycles of experimentation and computation to develop a first in silico model to describe the dynamics of HIV-1 spread in complex tissue. These analyses (i) revealed that 3D collagen environments restrict cell-free HIV-1 infection but promote cell-associated virus transmission and (ii) defined that cell densities in tissue dictate the efficacy of these transmission modes for virus spread. In this review, we discuss, in the context of the current literature, the implications of this study for our understanding of HIV-1 spread in vivo, which aspects of in vivo physiology this integrated experimental-computational analysis takes into account, and how it can be further improved experimentally and in silico.

Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection

Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called "multiscale model," formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. However, in general, PDE models are considerably more difficult to subject to mathematical and numerical analyses. In our recently reported study, we successfully derived a mathematically identical ODE model from a PDE model, which helps to overcome the limitations of the PDE model with regard to clinical data analysis. Here, we derive the basic reproduction number from the identical ODE model and provide insight into the global stability of all possible steady states of the ODE model.

Modelling heterogeneity in viral-tumour dynamics: The effects of gene-attenuation on viral characteristics

The use of viruses as a cancer treatment is becoming increasingly more robust; however, there is still a long way to go before a completely successful treatment is formulated. One major challenge in the field is to select which virus, out of a burgeoning number of oncolytic viruses and engineered derivatives, can maximise both treatment spread and anticancer cytotoxicity. To assist in solving this problem, an in-depth understanding of the virus-tumour interaction is crucial. In this article, we present a novel integro-differential system with distributed delays embodying the dynamics of an oncolytic adenovirus with a fixed population of tumour cells in vitro, allowing for heterogeneity to exist in the virus and cell populations. The parameters of the model are optimised in a hierarchical manner, the purpose of which is not to obtain a perfect representation of the data. Instead, we place our parameter values in the correct region of the parameter space. Due to the sparse nature of the data it is not possible to obtain the parameter values with any certainty, but rather we demonstrate the suitability of the model. Using our model we quantify how modifications to the viral genome alter the viral characteristics, specifically how the attenuation of the E1B 19 and E1B 55 gene affect the system performance, and identify the dominant processes altered by the mutations. From our analysis, we conclude that the deletion of the E1B 55 gene significantly reduces the replication rate of the virus in comparison to the deletion of the E1B 19 gene. We also found that the deletion of both the E1B 19 and E1B 55 genes resulted in a long delay in the average replication start time of the virus. This leads us to propose the use of E1B 19 gene-attenuated adenovirus for cancer therapy, as opposed to E1B 55 gene-attenuated adenoviruses.

Dynamics of lentiviral infection in vivo in the absence of adaptive immune responses

Understanding the dynamics of acute viral infection is crucial for developing strategies to prevent and control infection. In this study, lentiviral dynamics in a host without adaptive immunity were examined in order to determine kinetic parameters of infection and quantify the effect of neutralizing antibodies in preventing infection, using mathematical modeling of data from equine infectious anemia virus (EIAV) infection of horses with severe combined immunodeficiency (SCID). Estimated parameters were used to calculate the basic reproductive number and virus doubling time and found that the rate that antibodies neutralized virus was ~18 times greater than the virus clearance rate. These results establish EIAV replication kinetics in SCID horses and the minimal efficacy of antibodies that blocked infection. Furthermore, they indicate that EIAV is at most mildly cytopathic. This study advances our understanding of EIAV infection and may have important implications for the control of other viral infections, including HIV.

Duration of SHIV production by infected cells is not exponentially distributed: Implications for estimates of infection parameters and antiviral efficacy

The duration of the eclipse phase, from cell infection to the production and release of the first virion progeny, immediately followed by the virus-production phase, from the first to the last virion progeny, are important steps in a viral infection, by setting the pace of infection progression and modulating the response to antiviral therapy. Using a mathematical model (MM) and data for the infection of HSC-F cells with SHIV in vitro, we reconfirm our earlier finding that the eclipse phase duration follows a fat-tailed distribution, lasting 19 h (18–20 h). Most importantly, for the first time, we show that the virus-producing phase duration, which lasts 11 h (9.8–12 h), follows a normal-like distribution, and not an exponential distribution as is typically assumed. We explore the significance of this finding and its impact on analysis of plasma viral load decays in HIV patients under antiviral therapy. We find that incorrect assumptions about the eclipse and virus-producing phase distributions can lead to an overestimation of antiviral efficacy. Additionally, our predictions for the rate of plasma HIV decay under integrase inhibitor therapy offer an opportunity to confirm whether HIV production duration in vivo also follows a normal distribution, as demonstrated here for SHIV infections in vitro.

Global properties for an age-structured within-host model with Crowley–Martin functional response

Based on a multi-scale view, in this paper, we study an age-structured within-host model with Crowley–Martin functional response for the control of viral infections. By means of semigroup and Lyapunov function, the global asymptotical property of infected steady state of the model is obtained. The results show that when the basic reproductive number falls below unity, the infection dies out. However, when the basic reproductive number exceeds unity, there exists a unique positive equilibrium which is globally asymptotically stable. This model can be deduced to different viral models with or without time delay.

Large Variations in HIV-1 Viral Load Explained by Shifting-Mosaic Metapopulation Dynamics

The viral population of HIV-1, like many pathogens that cause systemic infection, is structured and differentiated within the body. The dynamics of cellular immune trafficking through the blood and within compartments of the body has also received wide attention. Despite these advances, mathematical models, which are widely used to interpret and predict viral and immune dynamics in infection, typically treat the infected host as a well-mixed homogeneous environment. Here, we present mathematical, analytical, and computational results that demonstrate that consideration of the spatial structure of the viral population within the host radically alters predictions of previous models. We study the dynamics of virus replication and cytotoxic T lymphocytes (CTLs) within a metapopulation of spatially segregated patches, representing T cell areas connected by circulating blood and lymph. The dynamics of the system depend critically on the interaction between CTLs and infected cells at the within-patch level. We show that for a wide range of parameters, the system admits an unexpected outcome called the shifting-mosaic steady state. In this state, the whole body’s viral population is stable over time, but the equilibrium results from an underlying, highly dynamic process of local infection and clearance within T-cell centers. Notably, and in contrast to previous models, this new model can explain the large differences in set-point viral load (SPVL) observed between patients and their distribution, as well as the relatively low proportion of cells infected at any one time, and alters the predicted determinants of viral load variation.

A novel metapopulation model of HIV suggests that within-host infections are characterized by a highly dynamic process of localized infection followed by clearance within T cell centers.

When a person is infected with HIV, the initial peak level of virus in the blood is usually very high before a lower, relatively stable level is reached and maintained for the duration of the chronic infection. This stable level is known as the set-point viral load (SPVL) and is associated with severity of infection. SPVL is also highly variable among patients, ranging from 100 to a million copies of the virus per mL of blood. The replicative capacity of the infecting virus and the strength of the immune response both influence SPVL. However, standard mathematical models show that variation in these two factors cannot easily reproduce the observed distribution of SPVL among patients. Standard models typically treat infected individuals as well-mixed systems, but in reality viral replication is localised in T-cell centres, or patches, found in secondary lymphoid tissue. To account for this population structure, we developed a carefully parameterised metapopulation model. We find the system can reach a steady state at which the viral load in the blood is relatively stable, representing SPVL, but surprisingly, the patches are highly dynamic, characterised by bursts of infection followed by elimination of virus due to localised host immune responses. Significantly, this model can reproduce the wide distribution of SPVLs found among infected individuals for realistic distributions of viral replicative capacity and strength of immune response. Our model can also be used in the future to understand other aspects of chronic HIV infection.

Dynamics of a diffusive age-structured HBV model with saturating incidence

In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain Ω ⊂ Rn and obtain an explicit formula for the basic reproductive number R0 of the model. Then we investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable, whereas if R0 > 1, then the infected steady state is globally asymptotically stable. In addition, when R0> 1, by constructing a suitable Lyapunov-like functional decreasing along the travelling waves to show their convergence towards two steady states as t tends to ∞, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results.

Notwithstanding Circumstantial Alibis, Cytotoxic T Cells Can Be Major Killers of HIV-1-Infected Cells

Several experiments suggest that in the chronic phase of human immunodeficiency virus type 1 (HIV-1) infection, CD8⁺ cytotoxic T lymphocytes (CTL) contribute very little to the death of productively infected cells. First, the expected life span of productively infected cells is fairly long, i.e., about 1 day. Second, this life span is hardly affected by the depletion of CD8⁺ T cells. Third, the rate at which mutants escaping a CTL response take over the viral population tends to be slow. Our main result is that all these observations are perfectly compatible with killing rates that are much faster than one per day once we invoke the fact that infected cells proceed through an eclipse phase of about 1 day before they start producing virus. Assuming that the major protective effect of CTL is cytolytic, we demonstrate that mathematical models with an eclipse phase account for the data when the killing is fast and when it varies over the life cycle of infected cells. Considering the steady state corresponding to the chronic phase of the infection, we find that the rate of immune escape and the rate at which the viral load increases following CD8⁺ T cell depletion should reflect the viral replication rate, ρ. A meta-analysis of previous data shows that viral replication rates during chronic infection vary between 0.5 ≤ ρ ≤ 1 day⁻¹. Balancing such fast viral replication requires killing rates that are several times larger than ρ, implying that most productively infected cells would die by cytolytic effects.

IMPORTANCE Most current data suggest that cytotoxic T cells (CTL) mediate their control of human immunodeficiency virus type 1 (HIV-1) infection by nonlytic mechanisms; i.e., the data suggest that CTL hardly kill. This interpretation of these data has been based upon the general mathematical model for HIV infection. Because this model ignores the eclipse phase between the infection of a target cell and the start of viral production by that cell, we reanalyze the same data sets with novel models that do account for the eclipse phase. We find that the data are perfectly consistent with lytic control by CTL and predict that most productively infected cells are killed by CTL. Because the killing rate should balance the viral replication rate, we estimate both parameters from a large set of published experiments in which CD8⁺ T cells were depleted in simian immunodeficiency virus (SIV)-infected monkeys. This confirms that the killing rate can be much faster than is currently appreciated.

Multiscale modeling of virus replication and spread

Replication and spread of human viruses is based on the simultaneous exploitation of many different host functions, bridging multiple scales in space and time. Mathematical modeling is essential to obtain a systems-level understanding of how human viruses manage to proceed through their life cycles. Here, we review corresponding advances for viral systems of large medical relevance, such as human immunodeficiency virus-1 (HIV-1) and hepatitis C virus (HCV). We will outline how the combination of mathematical models and experimental data has advanced our quantitative knowledge about various processes of these pathogens, and how novel quantitative approaches promise to fill remaining gaps.

A multi-scale mathematical modeling framework to investigate anti-viral therapeutic opportunities in targeting HIV-1 accessory proteins

Human immunodeficiency virus-1 (HIV-1) employs accessory proteins to evade innate immune responses by neutralizing the anti-viral activity of host restriction factors. Apolipoprotein B mRNA-editing enzyme 3G (APOBEC3G, A3G) and bone marrow stromal cell antigen 2 (BST2) are host resistance factors that potentially inhibit HIV-1 infection. BST2 reduces viral production by tethering budding HIV-1 particles to virus producing cells, while A3G inhibits the reverse transcription (RT) process and induces viral genome hypermutation through cytidine deamination, generating fewer replication competent progeny virus. Two HIV-1 proteins counter these cellular restriction factors: Vpu, which reduces surface BST2, and Vif, which degrades cellular A3G. The contest between these host and viral proteins influences whether HIV-1 infection is established and progresses towards AIDS. In this work, we present an age-structured multi-scale viral dynamics model of in vivo HIV-1 infection. We integrated the intracellular dynamics of anti-viral activity of the host factors and their neutralization by HIV-1 accessory proteins into the virus/cell population dynamics model. We calculate the basic reproductive ratio (Ro) as a function of host-viral protein interaction coefficients, and numerically simulated the multi-scale model to understand HIV-1 dynamics following host factor-induced perturbations. We found that reducing the influence of Vpu triggers a drop in Ro, revealing the impact of BST2 on viral infection control. Reducing Vif׳s effect reveals the restrictive efficacy of A3G in blocking RT and in inducing lethal hypermutations, however, neither of these factors alone is sufficient to fully restrict HIV-1 infection. Interestingly, our model further predicts that BST2 and A3G function synergistically, and delineates their relative contribution in limiting HIV-1 infection and disease progression. We provide a robust modeling framework for devising novel combination therapies that target HIV-1 accessory proteins and boost antiviral activity of host factors.

HIV-related hematological malignancies: a concise review

HIV (Human Immunodeficiency Virus) and its consequence, AIDS (acquired immunodeficiency syndrome) are responsible for a human tragedy of incalculable proportions. Patients afflicted by it are susceptible due to an early senescence of the immune system to opportunistic infections and malignancies. Since the introduction in 1996 of highly active anti-retroviral therapy (HAART), the landscape of malignancies associated to HIV/AIDS has changed in a significant manner as a direct result of significant improvement in the morbidity, mortality and life expectancy of HIV infected patients. While there has been a significant decrease in developed countries of malignancies such as Kaposi's sarcoma and Primary CNS lymphomas associated to the pre-HAART HIV-related immunodeficiency, hematological malignancies, particularly non-Hodgkin lymphomas continue to be the most common cancer-related cause of death in HIV infected individuals. This concise review of the subject highlights aspects of the natural history of HIV disease as it relates to the cause of malignancies with emphasis in the management and treatment of HIV-related hematological malignancies.

Disentangling the impact of within-host evolution and transmission dynamics on the tempo of HIV-1 evolution

OBJECTIVE

To determine how HIV-1 risk groups impact transmitted diversity and the tempo of viral evolution at a population scale.

METHODS

We investigated a set of previously described transmission chains (n = 70) using a population genetic approach, and tested whether the expected differences in proportions of multivariant transmissions are reflected by varying proportions of transmitted diversity between men having sex with men (MSM) and heterosexual (HET) subpopulations - the largest contributors to HIV spread. To assess evolutionary rate differences among the different risk groups, we compiled risk group datasets for subtypes A1, B and CRF01_AE, and directly compared the absolute substitution rate and its synonymous and non-synonymous components.

RESULTS

There was sufficient demographic signal to inform the transmission model in Bayesian evolutionary analysis by sampling trees using env data to compare the transmission bottleneck size between the MSM and HET risk groups. We found no indications for a different proportion of transmitted genetic diversity at the population level between these groups. In the direct rate comparisons between the risk groups, however, we consistently recovered a higher evolutionary rate in the male-dominated risk group compared to the HET datasets.

CONCLUSION

We find that the risk group composition affects the viral evolutionary rate and therefore potentially also the adaptation rate. In particular, risk group-specific sex ratios, and the variation in within-host evolutionary rates between men and women, impose evolutionary rate differences at the epidemic level, but we cannot exclude a role of varying transmission rates.

Simple mathematical models do not accurately predict early SIV dynamics

Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results suggest that, in order to appropriately model early HIV/SIV dynamics, additional factors must be considered in the model development. These may include variability in monkey susceptibility to infection, within-host competition between different viruses for target cells at the initial site of virus replication in the mucosa, innate immune response, and possibly the inclusion of several different tissue compartments. The sobering news is that while an increase in model complexity is needed to explain the available experimental data, testing and rejection of more complex models may require more quantitative data than is currently available.

Quantifying the turnover of transcriptional subclasses of HIV-1-infected cells

HIV-1-infected cells in peripheral blood can be grouped into different transcriptional subclasses. Quantifying the turnover of these cellular subclasses can provide important insights into the viral life cycle and the generation and maintenance of latently infected cells. We used previously published data from five patients chronically infected with HIV-1 that initiated combination antiretroviral therapy (cART). Patient-matched PCR for unspliced and multiply spliced viral RNAs combined with limiting dilution analysis provided measurements of transcriptional profiles at the single cell level. Furthermore, measurement of intracellular transcripts and extracellular virion-enclosed HIV-1 RNA allowed us to distinguish productive from non-productive cells. We developed a mathematical model describing the dynamics of plasma virus and the transcriptional subclasses of HIV-1-infected cells. Fitting the model to the data allowed us to better understand the phenotype of different transcriptional subclasses and their contribution to the overall turnover of HIV-1 before and during cART. The average number of virus-producing cells in peripheral blood is small during chronic infection. We find that a substantial fraction of cells can become defectively infected. Assuming that the infection is homogenous throughout the body, we estimate an average in vivo viral burst size on the order of 10⁴ virions per cell. Our study provides novel quantitative insights into the turnover and development of different subclasses of HIV-1-infected cells, and indicates that cells containing solely unspliced viral RNA are a good marker for viral latency. The model illustrates how the pool of latently infected cells becomes rapidly established during the first months of acute infection and continues to increase slowly during the first years of chronic infection. Having a detailed understanding of this process will be useful for the evaluation of viral eradication strategies that aim to deplete the latent reservoir of HIV-1.

Gaining a quantitative understanding of the development and turnover of different HIV-1-infected subpopulations of cells is crucial to improve the outcome of patients on combination antiretroviral therapy (cART). The population of latently infected cells is of particular interest as they represent the major barrier to a cure of HIV-1 infection. We developed a mathematical model that describes the dynamics of different transcriptionally active subclasses of HIV-1-infected cells and the viral load in peripheral blood. The model was fitted to previously published data from five chronically HIV-1-infected patients starting cART. This allowed us to estimate critical parameters of the within-host dynamics of HIV-1, such as the the number of virions produced by a single infected cell. The model further allowed investigation of HIV-1 dynamics during the acute phase. Computer simulations illustrate that latently infected cells become rapidly established during the first months of acute infection and continue to increase slowly during the first years of chronic infection. This illustrates the opportunity for strategies that aim to eradicate the virus during early cART as the pool of HIV-1 infected cells is substantially smaller during acute infection than during chronic infection.

Intracellular dynamics of HIV infection

Early studies of HIV infection dynamics suggested that virus-producing HIV-infected cells had an average half-life of approximately 1 day. However, whether this average behavior is reflective of the dynamics of individual infected cells is unclear. Here, we use HIV-enhanced green fluorescent protein (EGFP) constructs and flow cytometry sorting to explore the dynamics of cell infection, viral protein production, and cell death in vitro. By following the numbers of productively infected cells expressing EGFP over time, we show that infected cell death slows down over time. Although infected cell death in vivo could be very different, our results suggest that the constant decay of cell numbers observed in vivo during antiretroviral treatment could reflect a balance of cell death and delayed viral protein production. We observe no correlation between viral protein production and death rate of productively infected cells, showing that viral protein production is not likely to be the sole determinant of the death of HIV-infected cells. Finally, we show that all observed features can be reproduced by a simple model in which infected cells have broad distributions of productive life spans, times to start viral protein production, and viral protein production rates. This broad spectrum of the level and timing of viral protein production provides new insights into the behavior and characteristics of HIV-infected cells.

Immune activation promotes evolutionary conservation of T-cell epitopes in HIV-1

HIV, unlike other viruses, may benefit from immune recognition by preserving the sequence of its T cell epitopes, thereby enhancing transmission between cells.

The immune system should constitute a strong selective pressure promoting viral genetic diversity and evolution. However, HIV shows lower sequence variability at T-cell epitopes than elsewhere in the genome, in contrast with other human RNA viruses. Here, we propose that epitope conservation is a consequence of the particular interactions established between HIV and the immune system. On one hand, epitope recognition triggers an anti-HIV response mediated by cytotoxic T-lymphocytes (CTLs), but on the other hand, activation of CD4⁺ helper T lymphocytes (T_H cells) promotes HIV replication. Mathematical modeling of these opposite selective forces revealed that selection at the intrapatient level can promote either T-cell epitope conservation or escape. We predict greater conservation for epitopes contributing significantly to total immune activation levels (immunodominance), and when T_H cell infection is concomitant to epitope recognition (trans-infection). We suggest that HIV-driven immune activation in the lymph nodes during the chronic stage of the disease may offer a favorable scenario for epitope conservation. Our results also support the view that some pathogens draw benefits from the immune response and suggest that vaccination strategies based on conserved T_H epitopes may be counterproductive.

A key component of the immune response against viruses and other pathogens is the recognition of short foreign protein sequences called epitopes. However, viruses can escape the immune system by mutating, so epitopes should accumulate high levels of genetic variability. This has been documented in several human viruses, but in HIV, unexpectedly, epitopes tend to be relatively conserved. Here, we propose that this is a consequence of the peculiar interactions that occur between HIV and the immune system. As with other viruses, recognition of HIV epitopes promotes the activation of cytotoxic and helper T lymphocytes, which then orchestrate a cellular immune response. However, HIV infects helper T lymphocytes as their target cell in the body and does so more efficiently when these cells have been activated to participate in an immune response. Mathematical modeling showed that, in some cases, HIV may take advantage of immune activation, thus favoring epitope conservation. This should be more likely to occur with epitopes that trigger more vigorous T-cell responses, and during the process known as “trans-infection,” in which helper T lymphocytes are infected while being activated. Our results highlight the potential advantages of an HIV vaccination strategy based on epitopes that stimulate cytotoxic T lymphocytes without specifically stimulating helper T lymphocytes.

From molecular genetics to phylodynamics: evolutionary relevance of mutation rates across viruses

Although evolution is a multifactorial process, theory posits that the speed of molecular evolution should be directly determined by the rate at which spontaneous mutations appear. To what extent these two biochemical and population-scale processes are related in nature, however, is largely unknown. Viruses are an ideal system for addressing this question because their evolution is fast enough to be observed in real time, and experimentally-determined mutation rates are abundant. This article provides statistically supported evidence that the mutation rate determines molecular evolution across all types of viruses. Properties of the viral genome such as its size and chemical composition are identified as major determinants of these rates. Furthermore, a quantitative analysis reveals that, as expected, evolution rates increase linearly with mutation rates for slowly mutating viruses. However, this relationship plateaus for fast mutating viruses. A model is proposed in which deleterious mutations impose an evolutionary speed limit and set an extinction threshold in nature. The model is consistent with data from replication kinetics, selection strength and chemical mutagenesis studies.

Impaired immune evasion in HIV through intracellular delays and multiple infection of cells

With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8(+) cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.

Assessing the impact of adherence to anti-retroviral therapy on treatment failure and resistance evolution in HIV

The adherence of patients to therapy is a crucial factor for successful HIV anti-retroviral therapy. Imperfect adherence may lead to treatment failure, which can cause the emergence of resistance within viral populations. We have developed a stochastic model that incorporates compartments of latently infected cells and virus genotypes with different susceptibilities to three simultaneously used drugs. With this model, we study the impact of several key parameters on the probability of treatment failure, i.e. insufficient viral suppression, and the emergence of resistance. Specifically, we consider the impact of drug dosage, drug half-lives, fitness costs for resistance, different basic reproductive numbers of the virus and the influence of pre-existing mutations under various levels of adherence. Furthermore, we also investigate the influence of different temporal distributions of non-adherent days (drug holidays) during a treatment. Factors that promote resistance evolution include a high reproductive number, extended drug holidays and poor adherence. Pre-existing mutations only have a substantial effect if they confer resistance against more than one drug. Overall, our study highlights the importance of the interactions between imperfect adherence, pharmacodynamics, pharmacokinetics and latently infected cells for our understanding of drug resistance and therapy failure in HIV anti-retroviral therapy.

Global stability for an HIV-1 infection model including an eclipse stage of infected cells

We consider the mathematical model for the viral dynamics of HIV-1 introduced in Rong et al. (2007) [37]. One main feature of this model is that an eclipse stage for the infected cells is included and cells in this stage may revert to the uninfected class. The viral dynamics is described by four nonlinear ordinary differential equations. In Rong et al. (2007) [37], the stability of the infected equilibrium has been analyzed locally. Here, we perform the global stability analysis using two techniques, the Lyapunov direct method and the geometric approach to stability, based on the higher-order generalization of Bendixson's criterion. We obtain sufficient conditions written in terms of the system parameters. Numerical simulations are also provided to give a more complete representation of the system dynamics.

Virus replication strategies and the critical CTL numbers required for the control of infection

Vaccines that elicit protective cytotoxic T lymphocytes (CTL) may improve on or augment those designed primarily to elicit antibody responses. However, we have little basis for estimating the numbers of CTL required for sterilising immunity at an infection site. To address this we begin with a theoretical estimate obtained from measurements of CTL surveillance rates and the growth rate of a virus. We show how this estimate needs to be modified to account for (i) the dynamics of CTL-infected cell conjugates, and (ii) features of the virus lifecycle in infected cells. We show that provided the inoculum size of the virus is low, the dynamics of CTL-infected cell conjugates can be ignored, but knowledge of virus life-histories is required for estimating critical thresholds of CTL densities. We show that accounting for virus replication strategies increases estimates of the minimum density of CTL required for immunity over those obtained with the canonical model of virus dynamics, and demonstrate that this modeling framework allows us to predict and compare the ability of CTL to control viruses with different life history strategies. As an example we predict that lytic viruses are more difficult to control than budding viruses when net reproduction rates and infected cell lifetimes are controlled for. Further, we use data from acute SIV infection in rhesus macaques to calculate a lower bound on the density of CTL that a vaccine must generate to control infection at the entry site. We propose that critical CTL densities can be better estimated either using quantitative models incorporating virus life histories or with in vivo assays using virus-infected cells rather than peptide-pulsed targets.

In the search for vaccines that provide reliable protection against major diseases such as HIV-AIDS, TB and Malaria, there is now a focus on generating populations of antigen-specific cytotoxic T lymphocytes (CTL), immune cells that recognise and kill infected cells. However, we have little idea of the number or density of CTL a vaccine would need to elicit to provide sterilizing immunity to an infection in a given tissue. In this study we use mathematical models to understand how a virus's replication strategy influences the minimum density of CTL needed to provide immunity at an infection site. We show that traditional models that neglect the viral lifecycle within infected cells will underestimate this density. To illustrate, we use our modelling framework to estimate the CTL density needed to control the spread of virus at the very earliest stages of primary SIV infection in rhesus macaques.

The failure of R0

The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

Implications of CTL-mediated killing of HIV-infected cells during the non-productive stage of infection

Patients infected with HIV exhibit orders of magnitude differences in their set-point levels of the plasma viral load. As to what extent this variation is due to differences in the efficacy of the cytotoxic T lymphocyte (CTL) response in these patients is unclear. Several studies have shown that HIV-infected CD4⁺ T cells also present viral epitopes that are recognized by CTLs before the productive stage of infection, i.e., during the intracellular eclipse phase before the infected cell starts to produce new viral particles. Here, we use mathematical modeling to investigate the potential impact of early killing of HIV-infected cells on viral replication. We suggest that the majority of CTL-mediated killing could occur during the viral eclipse phase, and that the killing of virus-producing cells could be substantially lower at later stages due to MHC-I-down-regulation. Such a mechanism is in agreement with several experimental observations that include CD8⁺ T cell depletion and antiretroviral drug treatment. This indicates a potentially important role of CTL-mediated killing during the non-productive stage of HIV-infected cells.

Mapping the architecture of the HIV-1 Tat circuit: A decision-making circuit that lacks bistability and exploits stochastic noise

Upon infection of a CD4(+) T cell, HIV-1 appears to 'choose' between two alternate fates: active replication or a long-lived dormant state termed proviral latency. A transcriptional positive-feedback loop generated by the HIV-1 Tat protein appears sufficient to mediate this decision. Here, we describe a coupled wet-lab and computational approach that uses mathematical modeling and live-cell time-lapse microscopy to map the architecture of the HIV-1 Tat transcriptional regulatory circuit and generate predictive models of HIV-1 latency. This approach provided the first characterization of a 'decision-making' circuit that lacks bistability and instead exploits stochastic fluctuations in cellular molecules (i.e. noise) to generate a decision between an on or off transcriptional state.

Intracellular transactivation of HIV can account for the decelerating decay of virus load during drug therapy

Linking the intracellular transactivation circuit of HIV into a virus dynamics model can account for activation of infected cells and reversion into latency.

We hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than through extracellular stimuli.

This systems approach to modelling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.

The viral reservoir of latently infected cells is considered to be one of the major barriers for eradicating the virus from patients infected with HIV. During prolonged antiretroviral therapy, it has been shown that the pool of latently infected cells decays very slowly and at a decreasing rate. The underlying mechanisms causing this decelerating decay are still unclear (Lassen et al, 2004a, 2004b; Han et al, 2007). A recent study has shown that HIV can exhibit a switch-like behavior where infected cells can either be activated or become resting in a latent state (Weinberger et al, 2005). To investigate the effect of this switch-like behavior on the viral infection dynamics, we devise a new model that links the intracellular transactivation of the virus with the extracellular virus dynamics (Box 1). The model can explain the typical decelerating decay of HIV that is observed during antiretroviral therapy. We find that the activation of latently infected cells is governed by the basal transcription rate of the inserted provirus. Therefore, our analysis suggests that increasing the basal transcription rate of the HIV provirus could serve as a new therapeutic intervention for eradicating the pool of latently infected cells. In addition, our systems approach to modeling virus dynamics offers a promising framework for inferring the extracellular dynamics of cell populations from their intracellular reaction networks.

Basic virus dynamics models have been essential in understanding quantitative issues of HIV replication. However, several parts of the viral life cycle remain elusive. One of the most critical steps is the start of viral transcription, which is governed by the regulatory protein trans-activator of transcription (Tat) that induces a positive feedback loop. It has been shown that this feedback loop can alternate between two states leading to a transient activation of viral transcription. Using Monte Carlo simulations, we integrate the transactivation circuit into a new virus dynamics model having an age-dependent transactivation rate and reversion into latency. The cycling of infected cells between an activated and latent state results in the typical decelerating decay of virus load following therapy. Further, we hypothesize that the activation of latently infected cells is governed by the basal transcription rate of the integrated provirus rather than the intra- or extracellular environment. Finally, our systems approach to modeling virus dynamics offers a promising framework to infer the extracellular dynamics of cell populations from their intracellular reaction networks.